Step 1: Decode the sample rule.
For FALSE the code is $6,1,12,19,5$. Checking $F$ is the $6$th letter, $A$ the $1$st, $L$ the $12$th, $S$ the $19$th, $E$ the $5$th, the rule is simply each letter replaced by its alphabet position.
Step 2: Confirm the rule is positional.
Since every number equals the plain alphabet rank of its letter, we just convert each letter of the new word the same way.
Step 3: Convert L.
$L$ is the $12$th letter, so it becomes $12$.
Step 4: Convert O and G.
$O$ is the $15$th letter giving $15$, and $G$ is the $7$th giving $7$.
Step 5: Convert I and C.
$I$ is the $9$th letter giving $9$, and $C$ is the $3$rd giving $3$.
Step 6: Write the full code.
Reading the ranks in order, LOGIC becomes $12,15,7,9,3$.
\[ \boxed{12, 15, 7, 9, 3} \]